gf-3.1.6: lib/haskell/Numeral.hs
module Numeral (int2tree) where
import PGF
int2tree :: Int -> Tree
int2tree i =
if i < 1000000
then gf (int2numeral i)
else gf (int2digits i)
int2numeral :: Int -> GNumeral
int2numeral i = case tens i of
0:0:0:m@(_:_) -> Gnum (Gpot3 (s2s1000 m))
n:0:0:m@(_:_) -> Gnum (Gpot3plus (s2s1000 m) (s2s1000 [n]))
n1:n2:0:m@(_:_) -> Gnum (Gpot3plus (s2s1000 m) (s2s1000 [n1,n2]))
n1:n2:n3:m@(_:_) -> Gnum (Gpot3plus (s2s1000 m) (s2s1000 [n1,n2,n3]))
n -> Gnum (Gpot2as3 (s2s1000 n))
where
s2s1000 :: [Int] -> GSub1000
s2s1000 k = case k of
0:0:d:[] -> Gpot2 (s2s10 d)
n:0:d:[] -> Gpot2plus (s2s10 d) (s2s100 [n])
n1:n2:d:[] -> Gpot2plus (s2s10 d) (s2s100 [n1,n2])
n -> Gpot1as2 (s2s100 n)
s2s100 :: [Int] -> GSub100
s2s100 k = case k of
0:1:[] -> Gpot110 ;
1:1:[] -> Gpot111 ;
d:1:[] | digit d -> Gpot1to19 (s2d d)
0:d:[] | idigit d -> Gpot1 (s2d d)
n:d:[] | idigit d -> Gpot1plus (s2d d) (s2s10 n)
[n] -> Gpot0as1 (s2s10 n)
_ -> error $ "too many digits in " ++ show i
s2s10 :: Int -> GSub10
s2s10 k = case k of
1 -> Gpot01
_ | idigit k -> Gpot0 (s2d k)
_ -> error ("not a valid digit" ++ show k)
s2d :: Int -> GDigit
s2d d = case d of
2 -> Gn2
3 -> Gn3
4 -> Gn4
5 -> Gn5
6 -> Gn6
7 -> Gn7
8 -> Gn8
9 -> Gn9
_ -> error ("not a valid digit" ++ show d)
digit = flip elem [1 .. 9]
idigit = flip elem [0 .. 9]
int2digits :: Int -> GDigits
int2digits i =
let ([d],ds) = splitAt 1 (map dig (tens i)) in
foldr GIIDig (GIDig d) (reverse ds)
where
dig d = [GD_0,GD_1,GD_2,GD_3,GD_4,GD_5,GD_6,GD_7,GD_8,GD_9] !! d
tens n = let n' = div n 10 in mod n 10 : if n'==0 then [] else tens n'
----------------------------------------------------
-- below this line machine-generated by 'gf -output-format=haskell Numeral.gf'
----------------------------------------------------
----------------------------------------------------
-- automatic translation from GF to Haskell
----------------------------------------------------
class Gf a where
gf :: a -> Tree
fg :: Tree -> a
newtype GString = GString String deriving Show
instance Gf GString where
gf (GString x) = mkStr x
fg t =
case unStr t of
Just x -> GString x
Nothing -> error ("no GString " ++ show t)
newtype GInt = GInt Integer deriving Show
instance Gf GInt where
gf (GInt x) = mkInt x
fg t =
case unInt t of
Just x -> GInt x
Nothing -> error ("no GInt " ++ show t)
newtype GFloat = GFloat Double deriving Show
instance Gf GFloat where
gf (GFloat x) = mkDouble x
fg t =
case unDouble t of
Just x -> GFloat x
Nothing -> error ("no GFloat " ++ show t)
----------------------------------------------------
-- below this line machine-generated
----------------------------------------------------
data GDig =
GD_0
| GD_1
| GD_2
| GD_3
| GD_4
| GD_5
| GD_6
| GD_7
| GD_8
| GD_9
deriving Show
data GDigit =
Gn2
| Gn3
| Gn4
| Gn5
| Gn6
| Gn7
| Gn8
| Gn9
deriving Show
data GDigits =
GIDig GDig
| GIIDig GDig GDigits
deriving Show
data GNumeral = Gnum GSub1000000
deriving Show
data GSub10 =
Gpot0 GDigit
| Gpot01
deriving Show
data GSub100 =
Gpot0as1 GSub10
| Gpot1 GDigit
| Gpot110
| Gpot111
| Gpot1plus GDigit GSub10
| Gpot1to19 GDigit
deriving Show
data GSub1000 =
Gpot1as2 GSub100
| Gpot2 GSub10
| Gpot2plus GSub10 GSub100
deriving Show
data GSub1000000 =
Gpot2as3 GSub1000
| Gpot3 GSub1000
| Gpot3plus GSub1000 GSub1000
deriving Show
instance Gf GDig where
gf GD_0 = mkApp (mkCId "D_0") []
gf GD_1 = mkApp (mkCId "D_1") []
gf GD_2 = mkApp (mkCId "D_2") []
gf GD_3 = mkApp (mkCId "D_3") []
gf GD_4 = mkApp (mkCId "D_4") []
gf GD_5 = mkApp (mkCId "D_5") []
gf GD_6 = mkApp (mkCId "D_6") []
gf GD_7 = mkApp (mkCId "D_7") []
gf GD_8 = mkApp (mkCId "D_8") []
gf GD_9 = mkApp (mkCId "D_9") []
fg t =
case unApp t of
Just (i,[]) | i == mkCId "D_0" -> GD_0
Just (i,[]) | i == mkCId "D_1" -> GD_1
Just (i,[]) | i == mkCId "D_2" -> GD_2
Just (i,[]) | i == mkCId "D_3" -> GD_3
Just (i,[]) | i == mkCId "D_4" -> GD_4
Just (i,[]) | i == mkCId "D_5" -> GD_5
Just (i,[]) | i == mkCId "D_6" -> GD_6
Just (i,[]) | i == mkCId "D_7" -> GD_7
Just (i,[]) | i == mkCId "D_8" -> GD_8
Just (i,[]) | i == mkCId "D_9" -> GD_9
_ -> error ("no Dig " ++ show t)
instance Gf GDigit where
gf Gn2 = mkApp (mkCId "n2") []
gf Gn3 = mkApp (mkCId "n3") []
gf Gn4 = mkApp (mkCId "n4") []
gf Gn5 = mkApp (mkCId "n5") []
gf Gn6 = mkApp (mkCId "n6") []
gf Gn7 = mkApp (mkCId "n7") []
gf Gn8 = mkApp (mkCId "n8") []
gf Gn9 = mkApp (mkCId "n9") []
fg t =
case unApp t of
Just (i,[]) | i == mkCId "n2" -> Gn2
Just (i,[]) | i == mkCId "n3" -> Gn3
Just (i,[]) | i == mkCId "n4" -> Gn4
Just (i,[]) | i == mkCId "n5" -> Gn5
Just (i,[]) | i == mkCId "n6" -> Gn6
Just (i,[]) | i == mkCId "n7" -> Gn7
Just (i,[]) | i == mkCId "n8" -> Gn8
Just (i,[]) | i == mkCId "n9" -> Gn9
_ -> error ("no Digit " ++ show t)
instance Gf GDigits where
gf (GIDig x1) = mkApp (mkCId "IDig") [gf x1]
gf (GIIDig x1 x2) = mkApp (mkCId "IIDig") [gf x1, gf x2]
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "IDig" -> GIDig (fg x1)
Just (i,[x1,x2]) | i == mkCId "IIDig" -> GIIDig (fg x1) (fg x2)
_ -> error ("no Digits " ++ show t)
instance Gf GNumeral where
gf (Gnum x1) = mkApp (mkCId "num") [gf x1]
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "num" -> Gnum (fg x1)
_ -> error ("no Numeral " ++ show t)
instance Gf GSub10 where
gf (Gpot0 x1) = mkApp (mkCId "pot0") [gf x1]
gf Gpot01 = mkApp (mkCId "pot01") []
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "pot0" -> Gpot0 (fg x1)
Just (i,[]) | i == mkCId "pot01" -> Gpot01
_ -> error ("no Sub10 " ++ show t)
instance Gf GSub100 where
gf (Gpot0as1 x1) = mkApp (mkCId "pot0as1") [gf x1]
gf (Gpot1 x1) = mkApp (mkCId "pot1") [gf x1]
gf Gpot110 = mkApp (mkCId "pot110") []
gf Gpot111 = mkApp (mkCId "pot111") []
gf (Gpot1plus x1 x2) = mkApp (mkCId "pot1plus") [gf x1, gf x2]
gf (Gpot1to19 x1) = mkApp (mkCId "pot1to19") [gf x1]
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "pot0as1" -> Gpot0as1 (fg x1)
Just (i,[x1]) | i == mkCId "pot1" -> Gpot1 (fg x1)
Just (i,[]) | i == mkCId "pot110" -> Gpot110
Just (i,[]) | i == mkCId "pot111" -> Gpot111
Just (i,[x1,x2]) | i == mkCId "pot1plus" -> Gpot1plus (fg x1) (fg x2)
Just (i,[x1]) | i == mkCId "pot1to19" -> Gpot1to19 (fg x1)
_ -> error ("no Sub100 " ++ show t)
instance Gf GSub1000 where
gf (Gpot1as2 x1) = mkApp (mkCId "pot1as2") [gf x1]
gf (Gpot2 x1) = mkApp (mkCId "pot2") [gf x1]
gf (Gpot2plus x1 x2) = mkApp (mkCId "pot2plus") [gf x1, gf x2]
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "pot1as2" -> Gpot1as2 (fg x1)
Just (i,[x1]) | i == mkCId "pot2" -> Gpot2 (fg x1)
Just (i,[x1,x2]) | i == mkCId "pot2plus" -> Gpot2plus (fg x1) (fg x2)
_ -> error ("no Sub1000 " ++ show t)
instance Gf GSub1000000 where
gf (Gpot2as3 x1) = mkApp (mkCId "pot2as3") [gf x1]
gf (Gpot3 x1) = mkApp (mkCId "pot3") [gf x1]
gf (Gpot3plus x1 x2) = mkApp (mkCId "pot3plus") [gf x1, gf x2]
fg t =
case unApp t of
Just (i,[x1]) | i == mkCId "pot2as3" -> Gpot2as3 (fg x1)
Just (i,[x1]) | i == mkCId "pot3" -> Gpot3 (fg x1)
Just (i,[x1,x2]) | i == mkCId "pot3plus" -> Gpot3plus (fg x1) (fg x2)
_ -> error ("no Sub1000000 " ++ show t)